COS-MATH-171 – Example Timeline
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171 Calculus A: Example Timeline
• 43 lecture hours - 3 exam days = 40 lecture hours
• Approximated exam days: Mondays of weeks 4, 8, and 12
• 2 workshops per week
• Lectures 1–3
1. Review of power functions and polynomials, including end behavior and
graph structure
2. Review of rational functions, including asymptotes
3. Review of trigonometric functions, including amplitude and phase shift
(a) Review values of sine and cosine at standard reference angles
• Lectures 4–6
1. Review of exponential functions
2. Review of graphs and transformations
3. Logarithms
• Lectures 7–9
1. Horizontal line test and invertibility
2. Inverse functions, including arcsine, arccosine and arctangent
3. Graphs of inverse functions
4. Compositions (e.g., sin(arccos x))
• Exam #1 on or about Day 10 (beginning of Week 4)
1. Topics: functions, graphs, inverses
2. Early Alerts and Kudos
COS-MATH-171 – Example Timeline
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• Lectures 10–13
1. Limits
(a)
(b)
(c)
(d)
Graphical and numerical introduction
One-sided, two-sided
Limit Laws
Introduction to indeterminate forms via rational functions
• Lectures 14–16
1. Squeeze Theorem and its consequences, including limθ→0
is measured in radians
sin θ
θ
= 1 when θ
2. Limits at infinity
• Lectures 17–19
1. Continuity
(a) Extreme Value Theorem
(b) Intermediate Value Theorem
2. Definition of the derivative at a point
3. Interpretation of the derivative at a point
(a) Slope of secant line
(b) Rate of change (dimensional analysis?)
4. Derivatives of polynomials
• Exam #2 on or about Day 21 (end of Week 7/beginning of Week 8)
1. Topics: limits, continuity, definition and interpretation of the derivative,
derivatives of polynomials
2. Alerts and Kudos
COS-MATH-171 – Example Timeline
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• Lectures 20–23
1. Derivatives of sin(ωt), cos(ωt), ekt , bkt , cosh(kt), sinh(kt)
2. Linear approximation, differentials, and the equation of the tangent line
3. Derivative as a function
4. Critical points (including corners and cusps)
5. Fermat’s Theorem, Rolle’s Theorem, Mean Value Theorem
• Lectures 24–27
1. Arithmetic rules of differentiation (sum rule, constant factors rule, etc.)
2. Product Rule
3. Quotient Rule
4. Chain Rule
• Lectures 28–30
1. Derivatives of inverse functions, including ln x, logb x, arcsin x, arccos x and
arctan x
2. Implicit differentiation
• Exam #3 on or about Day 33 (end of Week 11/beginning of Week 12)
1. Topics: application and understanding of differentiation rules and techniques (including implicit differentiation), and consequences of differentiability (including knowledge and use of named theorems)
2. Alerts and Kudos
• Lectures 31–34
1. Logarithmic differentiation
2. Introduction to higher order derivatives, including concavity
COS-MATH-171 – Example Timeline
3. y 00 as acceleration (Newton’s Second Law, Speed up, slow down)
• Lectures 35–37
1. L’Hôpital’s Rule
2. Curve sketching
(a) Extrema
(b) Including First and Second Derivative Tests
• Lectures 38–40
1. Related Rates
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